Arrive at IAMM with host: Zachary Nicolaou

• Zachary Nicolaou

Travel to IAMM.

Seminar: Dr. George Stepaniants (Caltech)

• George Stepaniants

Room: 147 Title: Learning Memory and Material Dependent Constitutive Laws Abstract: The simulation of multiscale viscoelastic materials poses a significant challenge in computational materials science, requiring expensive numerical solvers that can resolve dynamics of material deformations at the microscopic scale. The theory of homogenization offers an alternative approach to modeling, by locally averaging the strains and stresses of multiscale materials. This procedure eliminates the smaller scale dynamics but introduces a history dependence between strain and stress that proves very challenging to characterize analytically. In the one-dimensional setting, we give the first full characterization of the memory-dependent constitutive laws that arise in multiscale viscoelastic materials. Using this theory, we develop a neural differential equation architecture, that simultaneously across a wide range of material microstructures, accurately predicts their homogenized constitutive laws, thus enabling us to simulate their deformations under forcing. We use the approximation theory of neural operators to provide guarantees on the generalization of our approach to unseen material samples. Bio: George Stepaniants is an NSF MSPRF postdoctoral fellow at the California Institute of Technology in the Department of Computing and Mathematical Sciences, working with Prof. Andrew Stuart. He received his PhD from the Massachusetts Institute of Technology (MIT) in 2024 in the Department of Mathematics, co-advised by Prof. Philippe Rigollet and Prof. Jörn Dunkel, and funded by the NSF GRFP and the MIT Presidential Fellowship. He was also part of the Interdisciplinary Doctoral Program in Statistics (IDPS) through the Institute for Data, Systems, and Society (IDSS). He received the Lawrence D. Brown PhD Student Award in 2025 from the Institute of Mathematical Statistics (IMS) for his statistical work on the optimal transport Gromov–Wasserstein method and its applications to metabolomics. Prior to MIT, he graduated in 2019 from the University of Washington (UW) with a Bachelor of Science in Mathematics and Computer Science, where he conducted research in the Department of Applied Mathematics with Prof. Nathan Kutz.

Research Meeting

• Adrian Del Maestro (University of Tennessee, Knoxville)

Room: 321

Research Meeting

• Ruixing Zhang (Department of Physics and Astronomy, University of Tennessee Knoxville)

Room: 323

Research Meeting

Research Meeting

Research Meeting

Research Meeting